Practically speaking non-controlling non-preferred equity of a private company is worth only whatever value those higher up the food chain assign it out of goodwill. Controlling interests can structure liquidation largely however they want...e.g. they can sell to themselves at a nominal price or they can sell their stock into a round and buy a Ferrari. Hollywood accounting happens outside of Hollywood.

There's nothing to be gained by forcing your way into equity unless you are funding. You're not and recognition that there are sound business reasons for a negative response to a request for equity is not a sign of lacking sophistication.

If it's on the table take it. If it's not figuring out the business reasons why is immensely valuable.

Good luck.